1) cos(2θ)+6sinēθ=4
cos(2θ)-4=-6(1-cosēθ)
cos(2θ)-4=-6+cosēθ
-cosēθ+cos2θ=-2
-cosēθ+cos2θ+2=0
-cosēθ+2cosēθ+1=0
cosθ(-cosθ+2cosθ)+1=0
-cosθ+2cosθ+1=0
cosθ+1=0
cosθ=-1
and, as you can imagine, that's not the answer in the back of the book :P
2) cosθ=sinθ
cosθ=(1-cosēθ)
cosθ+cosēθ=1
and I'm stuck there.

Any help would be appreciated - I'm having considerable trouble with these